Radiation imaging system, information processing apparatus for irradiation image, image processing method for radiation image, and program

ABSTRACT

A radiation imaging system includes a detector including a plurality of pixels which obtain pixel values corresponding to incident radiation transmitted through a subject, and an information processing unit configured to perform a process of estimating information on thicknesses of substances included in the subject using pixel values of an arbitrary one of the plurality of pixels, an average value of energy of radiation quanta of the arbitrary pixel calculated in accordance with the pixel values of the arbitrary pixel, a first table indicating the relationship between the pixel values of the arbitrary pixel and the thicknesses of the substances included in the subject, and a second table indicating the relationship between the average value of the energy of the radiation quanta of the arbitrary pixel and the thicknesses of the substances included in the subject.

TECHNICAL FIELD

The present invention relates to a radiation imaging system, aninformation processing apparatus which processes a radiation image, aninformation processing method for processing a radiation image, and aprogram.

BACKGROUND ART

As an imaging apparatus used for a medical image diagnosis and anon-destructive inspection using radiation (X-rays), a radiation imagingapparatus using a flat panel detector (FPD) formed of semiconductormaterial has been used. Such a radiation imaging apparatus may be usedas a digital imaging apparatus which captures still images and movingimages in the medical image diagnosis, for example.

Examples of the FPD include an integral sensor and a photon countingsensor. The integral sensor measures a total amount of charge generatedby incident radiation. The photon counting sensor discriminates energy(wavelengths) of incident radiation and counts the numbers of times theradiation is detected for individual energy levels. Specifically, sincethe photon counting sensor has energy resolution capability, the photoncounting sensor is expected to be applied to discrimination ofsubstances and generation of an image and measurement of bone density ina case where imaging is virtually performed with monoenergeticradiation. However, since the number of incident radiation quanta islarge, a high operation speed is required for individually counting theradiation quanta. Accordingly, it is difficult to realize the photoncounting sensor in an FPD having a large area.

Therefore, PTL 1 proposes a radiation imaging apparatus which realizesenergy resolution capability by estimating the number of radiationquanta and an average value of energy using average image densityinformation and distribution information of image density for eachpredetermined region. Specifically, PTL 1 discloses an informationprocessing method for estimating the number of radiation quanta and anaverage value of the energy using average image density information anddistribution information of image density for each predetermined regionand obtaining two types of image information, that is, the number ofradiation quanta and the average value of the energy of the radiationquanta. When the method disclosed in PTL 1 is employed, a sensor havingenergy resolution capability may he realized even in a case of a lowoperation speed when compared with the photon counting sensor.

On the other hand, PTL 2 discloses a technique of an energy subtractionmethod. When the energy subtraction method is employed, two images areobtained by irradiation of respective two types of energy and adifference process is performed on the two images which have beensubjected to a desired calculation so that the images of two substanceshaving different attenuation coefficients are generated in adiscrimination manner. The energy subtraction method utilizes aphenomenon in which different substances have different attenuationcoefficients indicating degrees of attenuation of radiation at timeswhen the radiation passes through the substances and the attenuationcoefficients depend on energy of the radiation. Furthermore, PTL 2further discloses a technique of dual-energy X-ray absorptiometry method(a DEXA method) which is a technique of measuring bone density utilizingthe same phenomenon. However, radiation imaging is performed twice usingtwo types of energy in the energy subtraction method and the DEXA methoddisclosed in PTL 2. Therefore, there arise problems in that artifact isgenerated due to a movement of a subject while energy is switched and inthat high speed switching of radiation energy is required. In terms ofthese problems, the processing method disclosed in PTL 1 is moreadvantageous since substances may be discriminated from each other byone radiation imaging using one type of energy.

CITATION LIST Patent Literature

PTL 1: Japanese Patent Laid-Open No. 2009-285356

PTL 2: Japanese Patent Laid-Open No. 2013-236962

SUMMARY OF INVENTION Technical Problem

However, PTL 1 does not disclose a method for obtaining information fordiscriminating two substances constituting a radiation image using twotypes of image information, that is, the obtained number of radiationquanta and the obtained average value of the energy the radiationquanta.

Solution to Problem

Accordingly, the present invention provides a technique of obtaininginformation for discriminating two substances included in a radiationimage of a subject without performing imaging by changing radiationenergy. A radiation imaging system according to the present inventionincludes a detector including a plurality of pixels which obtain pixelvalues corresponding to incident radiation transmitted through asubject, and an information processing unit configured to perform aprocess of estimating information on thicknesses of substances includedin the subject using pixel values of an arbitrary one of the pluralityof pixels, an average value of energy of radiation quanta of thearbitrary pixel calculated in accordance with the pixel values of thearbitrary pixel, a first table indicating the relationship between thepixel values of the arbitrary pixel and the thicknesses of thesubstances included in the subject, and a second table indicating therelationship between the average value of the energy of the radiationquanta of the arbitrary pixel and the thicknesses of the substancesincluded in the subject. An information processing apparatus whichprocesses a radiation image according to the present invention performsa process of estimating information on thicknesses of substancesincluded in a subject using pixel values of an arbitrary one of aplurality of pixels which obtain pixel values corresponding to incidentradiation transmitted through the subject, an average value of energy ofradiation quanta of the arbitrary pixel calculated in accordance withthe pixel values of the arbitrary pixel, a first table indicating therelationship between the pixel values of the arbitrary pixel and thethicknesses of the substances included in the subject, and a secondtable indicating the relationship between the average value of theenergy of the radiation quanta of the arbitrary pixel and thethicknesses of the substances included in the subject. An informationprocessing method for a radiation image according to the presentinvention includes performing a process of estimating information onthicknesses of substances included in a subject using pixel values of anarbitrary one of a plurality of pixels which obtain pixel valuescorresponding to incident radiation transmitted through the subject, anaverage value of energy of radiation quanta of the arbitrary pixelcalculated in accordance with the pixel values of the arbitrary pixel, afirst table indicating the relationship between the pixel values of thearbitrary pixel and the thicknesses of the substances included in thesubject, and a second table indicating the relationship between theaverage value of the energy of the radiation quanta of the arbitrarypixel and the thicknesses of the substances included in the subject. Aprogram that executes information processing on a radiation imageaccording to the present invention causes a computer to perform aprocess of estimating information on thicknesses of substances includedin a subject using pixel values of an arbitrary one of a plurality ofpixels which obtain pixel values corresponding to incident radiationtransmitted through the subject, an average value of energy of radiationquanta of the arbitrary pixel calculated in accordance with the pixelvalues of the arbitrary pixel, a first table indicating the relationshipbetween the pixel values of the arbitrary pixel and the thicknesses ofthe substances included in the subject, and a second table indicatingthe relationship between the average value of the energy of theradiation quanta of the arbitrary pixel and the thicknesses of thesubstances included in the subject.

Advantageous Effects of Invention

According to the present invention, information for discriminating twosubstances included in a subject may be obtained without performingimaging by changing radiation energy.

Further features of the present invention will become apparent from thefollowing description of exemplary embodiments with reference to theattached drawings.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a diagram schematically illustrating a functionalconfiguration of a radiation imaging system.

FIG. 2 is a flowchart illustrating a processing flow.

FIG. 3 is a graph illustrating linear attenuation coefficients of a boneand fat.

FIG. 4A is a table used by an estimation unit.

FIG. 4B is a table used by the estimation unit.

FIG. 5 is a diagram schematically illustrating a functionalconfiguration of a radiation imaging system.

FIG. 6 is a flowchart illustrating a processing flow.

FIG. 7 is a block diagram schematically illustrating the radiationimaging system.

DESCRIPTION OF EMBODIMENTS

Hereinafter, embodiments of the present invention will be described indetail with reference to the accompanying drawings. Note that, in thisspecification, examples of radiation include, in addition to an α-ray, aβ-ray, a γ-ray, and so on which are beams formed by particles (includingphotons) emitted due to radioactive decay, beams having energysubstantially the same as that of the beams formed by particles, such asan X-ray, a particle ray, and a cosmic ray.

First Embodiment

A configuration and a processing flow of a radiation imaging systemaccording to a first embodiment will now be described with reference toFIGS. 1 and 2, respectively. FIG. 1 is a diagram schematicallyillustrating a functional configuration of the radiation imaging systemaccording to the first embodiment. FIG. 2 is a flowchart illustrating aprocessing flow according to the first embodiment.

The radiation imaging system may include a radiation imaging apparatus10, a computer 13, a radiation control apparatus 12, and a radiationgeneration apparatus 11. The radiation generation apparatus 11 emitsradiation to a subject. The radiation imaging apparatus 10 includes adetector having a plurality of pixels which obtain pixel valuescorresponding to the radiation which enters through the subject. Thedetector obtains pixel values corresponding to the radiation whichenters through the subject. The computer 13 serving as an imageprocessing unit and/or an image processing apparatus of the presentinvention estimates an average value of energy of radiation quanta whichreach the detector using the pixel values and further estimatesinformation on thicknesses of substances constituting the subject. Theestimation will be described in detail hereinafter. Furthermore, thecomputer 13 supplies control signals to the radiation imaging apparatus10 and the radiation control apparatus 12 based on imaging informationinput by a photographer (not illustrated) through a control table (notillustrated) included in the computer 13. When receiving the controlsignal from the computer 13, the radiation control apparatus 12 controlsan operation of emitting radiation from a radiation source (notillustrated) included in the radiation generation apparatus 11 and anoperation of a irradiation field diaphragm mechanism (not illustrated).The detector of the radiation imaging apparatus 10 outputs an imagesignal corresponding to the radiation emitted from the radiationgeneration apparatus 11 controlled by the radiation control apparatus12. The output image signal is transmitted to the computer 13 afterbeing subjected to image processing, such as offset correction,performed by a signal processor. Here, a general wireless communicationor a general wired communication is used in the transmission. Thetransmitted image signal is subjected to required image processingperformed by the computer 13 before being displayed in a display unit(not illustrated) of the computer 13. Note that a pixel valueconstitutes a pixel signal.

The computer 13 includes, as a functional configuration thereof, a firstcalculation unit 131, a second calculation unit 132, and an estimationunit 133.

In step S201, radiation is emitted to the radiation imaging apparatus 10through the subject for a predetermined period of time so that thecomputer 13 obtains a plurality of digital image signals.

Next, principle of calculations performed in step S202 and step S203will be described. It is assumed here that the radiation emitted for thepredetermined period of time is fixed and the subject does not move. Anarbitrary one pixel is selected from among the obtained digital imagesignals. Although a digital signal (hereinafter referred to as a “pixelvalue”) obtained from the selected pixel is ideally fixed, the pixelvalue varies in time series in practice. The variation includes quantumnoise. The quantum noise is generated due to variation of the number ofradiation quanta (the number of X-ray photons, for example) per unittime. If the variation of the number of radiation quanta is consideredas occurrence probability of a discrete event per unit time, thevariation of the number of radiation quanta is based on Poissondistribution which is discrete probability distribution having aspecific random variable for counting discrete events generated at agiven time interval. As for the Poisson distribution, when a randomvariable which has a value of a natural number satisfies a desiredcondition in a condition in which a constants λ is larger than 0, therandom variable is based on the Poisson distribution of the parameter λ.Specifically, even in a case where images have the same average value ofpixel values, distribution of the pixel values of one of the imagesformed by radiation quanta having larger energy is larger than that ofthe other image. By utilizing this, the energy of the radiation quanta,such as X-ray photons, may be estimated.

Hereinafter, a method for estimating energy of radiation quanta will bedescribed using expressions. First, it is assumed that radiation isemitted to the radiation imaging apparatus 10 T times (T is a naturalnumber equal to or larger than 2) so that T digital image signals areobtained by the radiation imaging apparatus 10. Here, assuming that apixel value of a pixel of a t-th digital image signal (t is a naturalnumber equal to or larger than 2 and equal to or smaller than T) isdenoted by “I(t)”, the total number of radiation quanta which havereached the pixel and absorbed by the pixel is denoted by “N”, and anaverage value of the energy of the radiation quanta is denoted by“E_(Ave)”, Expression (1) below is obtained.

E _(Ave) ×N=ΣI(t)   (1)

According to Expression (1), assuming that an arithmetic average of thenumbers of radiation quanta which have reached and which have absorbedby the pixel of a single digital image signal is denoted by “n_(Ave)”,Expression (2) below is obtained.

n _(Ave) =N/T=ΣI(t)/E _(Ave) /T   (2)

Furthermore, according to Expression (1), assuming that sample varianceof the numbers of radiation quanta which have reached and which haveabsorbed by the pixel of the single digital image signal is denoted by“n_(Var)”, Expression (3) below is obtained.

n _(Var) Σ[{I(t)/E _(Ave) −n _(Ave)}² ]/T   (3)

Here, in the Poisson distribution, an expected value and variance areequal to the parameter λ. Furthermore, as the number of samples isincreased, the arithmetic average becomes close to the expected valueand the sample variance becomes close to the variance. Therefore,assuming that the number of samples is sufficiently large (preferablyinfinite) and the arithmetic average n, of the numbers of radiationquanta and the sample variance n_(Var) of the numbers of radiationquanta are approximated so as to be equal to each other, Expression (4)is obtained since Expressions (2) and (3) are equal to each other.

E _(Ave) =Σ{I(t)² }/Σ{I(t)}−Σ{I(t)}/T   (4)

In this way, an average value E_(Ave) of the energy of the radiationquanta which have reached the pixel and which have been absorbed by thepixel is estimated and calculated using the pixel value I(t) of thepixel of the arbitrary t-th digital image signal.

Furthermore, assuming that the arithmetic average of the pixel valuesI(t) is denoted by “I_(Ave)”, an arithmetic average I_(Ave) isrepresented by Expression (5) below using the arithmetic average n_(Ave)of the number of radiation quanta.

I _(Ave) =n _(Avee) ×E _(Ave)   (5)

Furthermore, assuming that sample variance of the pixel values isdenoted by “I_(Var)”, the sample variance I_(Var) of the pixel values isrepresented by Expression (6) below using the sample variance n_(Var) ofthe numbers of radiation quanta.

I _(Var) =n _(Var) ×E _(Ave) ²   (6)

Accordingly, an average value E of the energy of the radiation quantawhich have reached the pixel and which have absorbed by the pixel isalso represented by Expression (7) below.

E _(Ave) =I _(Var) /I _(Ave)   (7)

In step S202, the first calculation unit 131 calculates the samplevariance I_(Var) of the pixel values of the arbitrary pixel using thepixel values I(t) of the arbitrary pixel in accordance with Expression(8) below. Although the sample variance is used as variance in thisembodiment, unbiased variance may be used. Furthermore, although anarithmetic average I_(Ave) of the pixel values I(t) is used as anaverage of pixel values, the present invention is not limited to this.

$\begin{matrix}\lbrack {{Math}.\mspace{14mu} 1} \rbrack & \; \\{I_{var} = {{\frac{1}{T}\Sigma \; {I(t)}^{2}} - \lbrack {\frac{1}{T}\Sigma \; {I(t)}} \rbrack^{2}}} & (8)\end{matrix}$

In step S203, the second calculation unit 132 calculates the averagevalue E_(Ave) of the energy of the radiation quanta of the arbitrarypixel using the sample variance I_(Var) of the pixel values of thearbitrary pixel in accordance with Expression (9) below calculated usingExpression (7). Here, a is an arbitrary constant used to performconversion between a pixel value and a unit of energy. Although thesample variance is used as variance in this embodiment, unbiasedvariance may be used.

$\begin{matrix}\lbrack {{Math}.\mspace{14mu} 2} \rbrack & \; \\{E_{Ave} = {\alpha \frac{I_{var}}{I_{Ave}}}} & (9)\end{matrix}$

In the following steps, information on thicknesses of the substanceswhich constitute the subject are estimated using the average value ofthe energy of the radiation quanta of the arbitrary pixel calculated instep S202 and step S203 and the pixel values of the arbitrary pixel.Note that, for simplicity of description, it is assumed that a substance(a second constitutive substance) other than a bone (a firstconstitutive substance) in the substances included in a human bodyserving as an example of the subject is fat. Note that the first andsecond constitutive substances are different from each other. Althoughthe substances other than a bone include fat, muscle, internal organs,and water, these substances have linear attenuation coefficients similarto one another when compared with that of the bone. FIG. 3 is a graphillustrating linear attenuation coefficients of a bone and fat. Althoughdescription will be made using the linear attenuation coefficients of abone and fat hereinafter, two arbitrary linear attenuation coefficientsare used depending on diagnosis usage or constitutive substances of thesubject.

In step S204, the estimation unit 133 estimates a thickness of thesubject and a mix ratio of the substances included in the subject usingthe average value E_(Ave) of the energy of the radiation quanta of thearbitrary pixel and the arithmetic average I_(Ave) of the pixel valuesof the arbitrary pixel calculated using the pixel values of thearbitrary pixel. Here, the estimation unit 133 may estimate thethickness of the subject and the mix ratio of the substances included inthe subject using a table illustrated in FIG. 4A. FIG. 4A is a firsttable indicating the relationship among a thickness d of the subject, amix ratio γ of the substances included in the subject, and thearithmetic average I_(Ave) of the pixel values of the arbitrary pixel.Note that, in a case where the mix ratio γ is 1, the subject isconstituted only by bones (the first constitutive substance), whereas ina case where the mix ratio γ is 0, the subject is constituted only byfat (the second constitutive substance). The first table is preferablyobtained by experiment in advance. The first table may be calculated inadvance in accordance with Expression (10) below. It is assumed herethat a mass attenuation coefficient of a hone at a time when theradiation energy is E[kev] is denoted by “μ₁(E)”, a linear attenuationcoefficient of fat at a time when the radiation energy is E[kev] isdenoted by “μ₂(E)”, a thickness of the subject is denoted by “d”, andthe mix ratio of the substances included in the subject is denoted by“γ”. Furthermore, rates (energy spectra) of the numbers of radiationquanta of energy of radial rays before the radial rays pass the subjectare denoted by “n(E)”. In step S204, the estimation unit 133 performs acalculation using Expression (10) below so as to obtain the thickness dof the subject and the mix ratio γ. Here, “β” denotes an arbitrarycoefficient used to convert energy into a pixel value.

[Math. 3]

I _(Ave)=β∫₀ ^(∞) n(E)e ^(−μ) ¹ ^((E)dγ−μ) ² ^((E)d(1−γ)) EdE   (10)

Note that “n(E)” is preferably measured in advance using a commerciallyavailable spectrometer. Since a simple expression for obtaining anenergy spectrum is publicly available, the energy spectrum may becalculated using the simple expression in accordance with conditions ofa tube voltage, an additional filter, and the like at a time whenradiation is emitted. Furthermore, “β” is determined based oncharacteristics of a scintillator used in the radiation imagingapparatus 10 and characteristics of a system gain.

The estimation unit 133 may estimate the thickness of the subject andthe mix ratio of the substances included in the subject in accordancewith a table illustrated in FIG. 4B. FIG. 4B is a second tableindicating the relationship among the thickness d of the subject, themix ratio γ of the substances included in the subject, and the averagevalue E_(Ave) of the energy of the radiation quanta of the arbitrarypixel. The second table is also preferably obtained by experiment inadvance. The second table may be calculated in advance in accordancewith. Expression (11) below.

$\begin{matrix}\lbrack {{Math}.\mspace{14mu} 4} \rbrack & \; \\{E_{Ave} = \frac{I_{Ave}}{\beta {\int_{0}^{\infty}{{n(E)}e^{{{- {\mu_{1}{(E)}}}d\; \gamma} - {{\mu_{2}{(E)}}{d{({1 - \gamma})}}}}{dE}}}}} & (11)\end{matrix}$

The estimation unit 133 estimates thicknesses of the substances and themix ratio of the substances included in the subject which satisfy thecalculated average value E_(Ave) of the energy of the radiation quantaof the arbitrary pixel and the calculated arithmetic average I_(Ave) ofthe pixel values of the arbitrary pixel using the tables illustrated inFIGS. 4A and 4B.

Hereinafter, the estimation performed in a case where the arithmeticaverage I_(Ave) of the pixel values of the arbitrary pixel calculatedfrom the pixel values of the arbitrary pixel is i₃ of FIG. 4A and thecalculated average value E_(Ave) of the energy of the radiation quantaof the arbitrary pixel is e₄ of FIG. 4B will be described as an example.First, a combination of a thickness d of the subject and a mix ratio γwhich satisfies i₃ is retrieved from the first table in FIG. 4A. In thiscase, such combinations which satisfy i₃ are included in a region 401.Thereafter, a combination of a thickness d of the subject and a mixratio γ which satisfies e₄ is retrieved from the second table in FIG.4B. In this case, such combinations which satisfy e₄ are included in aregion 402. Finally, a combination of a thickness d of the subject and amix ratio γ which satisfies both of the regions 401 and 402 isretrieved. In this case, a combination of a thickness d₄ of the subjectand a mix ratio γ₄ satisfies both of the regions 401 and 402. Asdescribed above, since the two tables are used, the thickness of thesubject and the mix ratio of the two substances included in the subjectmay be estimated. Although the tables have six rows and six columns asan example in this embodiment, larger tables are preferably used inpractice. Furthermore, in a case where a plurality of results whichsatisfy both of the regions 401 and 402 are obtained in adjacentnumerical values, a combination of the smallest thickness d and thesmallest mix ratio γ is obtained taking influence of scattered radiationinto consideration. In actual imaging, a pixel value may be larger thana normal value due to the influence of scattered radiation. Therefore,in the case where a plurality of results which satisfy both of theregions 401 and 402 are obtained in adjacent numerical values, athickness d and a mix ratio γ which attain the largest calculatedaverage value E_(Ave) of the energy of the radiation quanta of thearbitrary pixel and the largest calculated arithmetic average of thepixel values of the arbitrary pixel are selected.

By performing the process from step S201 to step S204 described above,information on the thicknesses of the substances included in the subjectand information on a component ratio may be estimated. According to thisembodiment, the information on the thicknesses of the two differentsubstances included in the subject and the information on the componentratio of the substances may be estimated without changing radiationenergy in imaging. Accordingly, information for discriminating twosubstances included in a radiation image which may be applied to acomplicated radiographic system in general imaging and fluorography maybe obtained.

Although information on a bone and fat in a human body are estimatedusing the human body as the subject as an example in this embodiment,the present invention is not limited to this. For example, informationon a contrast agent and a human body may be estimated so that visibilityof distribution of the contrast agent is improved and an amount of thecontrast agent to he used is reduced. Furthermore, information on aguide wire and a human body may be estimated so that visibility of theguide wire is improved, and accordingly, security of a patient during anoperation may be ensured and a burden of a doctor during an operationmay be reduced. In this way, information on a thickness and informationon density of at least one of arbitrary different types of twosubstances may be obtained irrespective of a type of substance in thepresent invention.

Furthermore, a value BMD [g/cm²] corresponding to bone density may beestimated by using density ρ₁ [g/cm³] and a thickness d [cm] of the oneand a mix ratio γ, for example.

Furthermore, although information on the thicknesses and the mix ratioof the substances included in the subject are estimated in thisembodiment, the present invention is not limited to this. For example,if bone density and fat density may not be obtained or are unknown, thethicknesses d of the substances included in the subject may bemultiplied by the density p so as to obtain a value pd. For example,first information on a thickness and density of the first constitutivesubstance is represented by “ρ₁d₁” and second information on a thicknessand density of the second constitutive substance is represented by“ρ₂d₂”. Here, it is assumed that a mass attenuation coefficient of abone obtained when radiation energy is denoted by “E[kev]” is denoted by“μ(E)₁”, a thickness of the bone is denoted by “d₁”, and density of thebone is denoted by “ρ₁”. In addition, it is assumed that a massattenuation coefficient of fat obtained when radiation energy is denotedby “E[kev]” is denoted by “μ(E)₂”, a thickness of the fat is denoted by“d₂”, and density of the fax is denoted by “ρ₂”. The estimation unit 133estimates an arithmetic average of the pixel values of the arbitrarypixel by performing calculation using Expression (12) below. Note that,although the arithmetic average i_(Ave) of the pixel values I(t) isestimated as an average of the pixel values, the present invention isnot limited to this.

[Math. 5]

i _(Ave)=β∫₀ ^(∞) n(E)e ^(−μ(E)) ¹ ^(ρ) ¹ ^(d) ¹ ^(−μ(E)) ² ^(ρ) ² ^(d)² EdE   (12)

Furthermore, the estimation unit 133 estimates an average value e_(Ave)of the energy of the radiation quanta of the arbitrary pixel byperforming calculation using Expression (13) below. Note that, althoughthe arithmetic average i_(Ave) of the pixel values I(t) is estimated asan average of pixel values, the present invention is not limited tothis.

$\begin{matrix}\lbrack {{Math}.\mspace{14mu} 6} \rbrack & \; \\{e_{Ave} = \frac{i_{Ave}}{\beta {\int_{0}^{\infty}{{n(E)}e^{{{- {\mu {(E)}}_{1}}\rho_{1}d\; 1} - {{\mu {(E)}}_{2}\rho_{2}d_{2}}}{dE}}}}} & (13)\end{matrix}$

Then the estimation unit 133 uses “ρ₁” and “i_(Ave)” instead of “γ” and“I_(Ave)” of FIG. 4A and uses “ρ₂” and “e_(Ave)” instead of “γ” and“E_(Ave)” of FIG. 4B so as to estimate information on thicknesses anddensities of the substances included in the subject. Specifically, inthe present invention, the estimation unit 133 may use the first tableindicating the relationship between the arithmetic average I_(Ave) ofthe pixel values of the arbitrary pixel and the thicknesses d of thesubstances included in the subject for the estimation process.Furthermore, the estimation unit 133 may use the second table indicatingthe relationship between the calculated average value E_(Ave) of theenergy of the radiation quanta of the arbitrary pixel and thethicknesses d of the substances included in the subject for theestimation process. Then the estimation unit 133 estimates informationon the thicknesses of the substances included in the subject using thearithmetic average I_(Ave) of the pixel values of the arbitrary pixel,the arithmetic average I_(Ave) of the pixel values of the arbitrarypixel, the first table, and the second table.

Furthermore, although the sample variance and the arithmetic average arecalculated using a plurality of pixel values obtained in time series andan average value of the energy of the radiation quanta is estimated inthis embodiment, the present invention is not limited to this. Forexample, a case of pixel values of an arbitrary one of a plurality ofpixels arranged in two-dimensional space arrangement positions in amatrix having an X axis indicating columns and a Y axis indicating rowswill be considered. In this case, the average value of the energy of theradiation quanta may be estimated after sample variance and anarithmetic average of the pixel values of the arbitrary pixel arecalculated using pixel values of a plurality of surrounding pixels. Bythis, an energy image may be calculated from a single still image.

Furthermore, although the arithmetic average and the sample variancecalculated using the pixel values of the arbitrary pixel are used toobtain the average value E_(Ave) of the energy of the radiation quantaof this embodiment, the present invention is not limited to this. Asdescribed below, the average value of the energy of the radiation quantais calculated based on the pixel values of the arbitrary pixel, andtherefore, an amount of temporal and/or spatial change of a pixel valueof the arbitrary pixel may be used for the calculation, for example.

In actual radiation imaging, the subject may move while a plurality ofimages are captured (or a plurality of digital image signals areobtained by a radiation imaging apparatus 10). This happens in a casewhere imaging of an organ having a motion, such as a heart, isperformed, a case where fluoroscopic radiography is performed during anoperation, and the like. If a subject has a motion, the number of X-rayphotons which is an example of the number of radiation quanta whichreach a certain pixel is changed while the radiation imaging apparatus10 outputs a plurality of image data. Specifically, the parameter λ, ofthe Poisson distribution is changed. Accordingly, artifact is generatedin an image generated using the average value of the energy, andtherefore, diagnosis performance is degraded.

Therefore, it is preferable that the energy of the radiation quanta inthe arbitrary pixel is estimated using an amount of temporal and/orspatial change of a pixel value of the arbitrary pixel when the averagevalue of the energy of the radiation quanta in the arbitrary pixel isestimated. Here, the amount of temporal change of a pixel value means adifference between a pixel value of a pixel corresponding to (a pixel ina position the same as or in the vicinity of) the arbitrary pixel in aframe different from a frame in which the arbitrary pixel is specifiedand the pixel value of the arbitrary pixel. Furthermore, the amount ofspatial change of a pixel value means a difference between a pixel valueof a pixel positioned adjacent to or in the vicinity of the arbitrarypixel in the frame in which the arbitrary pixel is specified and thepixel value of the arbitrary pixel. The amount of temporal and spatialchange means mix of the means described above. Note that the number ofpixel values of the arbitrary pixel and the number of pixel values of apixel which is compared with the arbitrary pixel may be single orplural. In a case of a plurality of pixels, a representative value ofthe pixels (for example, a value obtained by performing a recursivefilter process or an averaging process on the values of the arbitrarypixel) is determined as the pixel value. Note that, although thedifferent frame described above used when the amount of temporal changeis to be obtained is preferably adjacent to the specific frame in a timeaxis, the different frame may be separated from the specific frame to adegree in which the effect is not degraded. Furthermore, although thearbitrary pixel and the different pixel are preferably adjacent to eachother when the amount of spatial change is to be obtained, the pixelsmay be separated from each other to a degree in which the effect is notdegraded. A range in which the effect is not degraded in despite of theseparation is referred to as an arbitrary range which includes some ofall pixel values used in signal processing. By using the change amount,error of the estimation of the average value of the energy of thearbitrary pixel may be suppressed.

More specifically, the present invention is based on a concept in whichthe sample variance of the pixel values is seen to be a half of squareof the amount of temporal and/or spatial change of the pixel value ofthe arbitrary pixel and the energy of the radiation quantum in thearbitrary pixel is approximated. In particular, the present invention isbased on a concept in which the sample variance of the pixel values isseen to be a half of square of a difference between the pixel value ofthe arbitrary pixel and the pixel value of the pixel in the position thesame as the position of the arbitrary pixel in the different frame andthe energy of the radiation quantum in the arbitrary pixel isapproximated. Then averaging is performed using the approximated energyof the radiation quantum of the arbitrary pixel so that the averagevalue of the energy of the radiation quantum of the arbitrary pixel isobtained. The energy of the radiation quantum in the arbitrary pixel haslarge error only when an expected value which is equal to the parameterλ of the Poisson distribution is changed. Accordingly, the generation ofartifact may be suppressed.

Furthermore, the average value of the energy of the radiation quanta maybe estimated using the energy of the radiation quanta obtained bycounting the numbers of detection in a plurality of energy levels foreach arbitrary pixel using a photon counting sensor as a detector, forexample. In this case, the pixel value of the arbitrary pixel in thepresent invention may include a pixel value of an arbitrary pixel in thephoton counting sensor.

Second Embodiment

In a second embodiment, a method for generating pixel values ofindividual substances using information on thicknesses of the substancesincluded in a subject obtained in the first embodiment will bedescribed. Hereinafter, a method for generating an image of a human bone(a first constitutive substance) and an image of portions other than abone in a discrimination manner will be described as an example withreference to FIGS. 5 and 6. FIG. 5 is a diagram schematicallyillustrating a functional configuration of a radiation imaging systemaccording to the second embodiment. FIG. 6 is a flowchart illustrating aprocessing flow according to the second embodiment. Note that functionalconfigurations and processing steps which are the same as those of thefirst embodiment are denoted by reference numerals the same as those ofthe first embodiment, and detailed descriptions thereof are omitted.

A pixel value generation unit 14 of FIG. 5 generates substance pixelvalues of the individual substances based on information on thethicknesses of the substances included in the subject and a mix ratio.The pixel value generation unit 14 includes a first pixel valuegeneration unit 141 and a second pixel value generation unit 142. Thefirst pixel value generation unit 141 generates a pixel value of a bone(a first pixel value) based on information on a thickness of the bone(the first constitutive substance) and a mix ratio (first information).The second pixel value generation unit 142 generates a pixel value offat (a second pixel value) based on information on a thickness of thefat (the second constitutive substance) and a mix ratio (secondinformation). Note that, for simplicity of description, as with thefirst embodiment, it is assumed that an image obtained by visualizingthe substance other than the bone in the substances included in thesubstance is determined as a fat image. Although the substance otherthan the bone includes fat, muscle, internal organs, and water, thesesubstances have linear attenuation coefficients similar to one anotherwhen compared with that of a bone.

In step S205 of FIG. 6, a pixel value (a first pixel value) of the boneis obtained using a calculation in accordance with Expression (14) belowbased on the first information obtained in the process from step S201 tostep S204.

[Math. 7]

I ₁=β∫₀ ^(∞) n(E)e ^(−μ) ¹ ^((E)dγ) EdE   (14)

In step S206, a pixel value (a second pixel value) I₂ of the fat iscalculated using a calculation in accordance with Expression (15) belowbased on the second information obtained in the process from step S201to step S204.

[Math. 8]

I ₂=β∫₀ ^(∞) n(E)e ^(−μ) ² ^((E)d(1−γ)) EdE   (15)

By performing the process described above, substance pixel values of theindividual two substances included in the subject may be generated.

Although the method for generating pixel values of the bone and the fatin the human body serving as the subject is described as an example inthis embodiment, the present invention is not limited to this. Forexample, information on a contrast agent and a human body may beestimated so that visibility of distribution of the contrast agent isimproved and an amount of the contrast agent to he used is reduced.Furthermore, if a pixel value of the contrast agent is generated, animage equivalent to a digital subtraction angiography image may begenerated without capturing an image before the contrast agent isinjected, and therefore, a relative positional change between a subjectand a radiation imaging apparatus during photographing may be copedwith. Furthermore, information on a guide wire and a human body may beestimated so that visibility of the guide wire is improved, andaccordingly, security of a patient during an operation is ensured and aburden of a doctor during an operation is reduced. In this way, thepixel values of the two arbitrary types of substance may be generatedirrespective of types of substance in the present invention.Furthermore, in a case where pixel values of all the two types ofsubstance are not required, that is, in a case where only a pixel valueof the bone is required or a case where only a pixel value of thecontrast agent is required, a corresponding one of the processes in stepS205 and step S206 may be omitted. Note that the pixel values obtainedin Expressions (14) and (15) correspond to a pixel value obtained whenonly a bone is virtually captured and a pixel value obtained when onlyfat is virtually captured, respectively, by the radiation imagingapparatus.

Furthermore, the pixel values may be generated by performingcalculations in accordance with Expression (16) and (17) below using anaverage (effective energy) E_(eff) of energy spectra of emittedradiation.

[Math. 9]

I ₁ =βe ^(−μ) ¹ ^((E) ^(eff) ^()d) ¹ ^(γ)  (16)

[Math. 10]

I ₂ =βe ^(−μ) ² ^((E) ^(eff) ^()d) ² ^((1−γ))   (17)

In this way, the calculation may be simplified using the effectiveenergy of the emitted radiation.

Furthermore, when arbitrary monochromatic radiation energy E_(mono) isset, a pixel value of energy virtually having an arbitrary spectrum maybe generated in accordance with a calculation of Expression (18) below.

[Math. 11]

I(E _(mono))=βe ^(−μ) ¹ ^((E) ^(mono) ^()d) ¹ ^(γ−μ) ² ^((E) ^(mono)^()d) ² ^((1−γ))   (18)

It is assumed that a linear attenuation coefficient of an iodinatedcontrast agent is denoted by “μ₁”, a linear attenuation coefficient ofthe human body is denoted by “μ₂”, a thickness of the iodinated contrastagent is denoted by “d₁”, a thickness of the human body is denoted by“d₂”, and a mix ratio between the iodinated contrast agent and the humanbody is denoted by “γ”, and contrast between the iodinated contrastagent and other substances is to be improved. In this case, since theiodinated contrast agent has a K absorption edge at 33.2 keV, thecalculation is performed while arbitrary monochromatic radiation energyE_(mono) of 33.2 keV is set.

Furthermore, the various pixel values may be generated by performingcalculations in accordance with Expressions (19) and (20) below using anarithmetic average I_(Ave) of pixel values based on obtained pixelvalues I(t).

$\begin{matrix}\lbrack {{Math}.\mspace{14mu} 12} \rbrack & \; \\{I_{1} = {{{Ln}( I_{Ave} )}\frac{{\mu_{1}( E_{eff} )}d\; \gamma}{{{\mu_{1}( E_{eff} )}d\; \gamma} + {{\mu_{2}( E_{eff} )}{d( {1 - \gamma} )}}}}} & (19) \\\lbrack {{Math}.\mspace{14mu} 13} \rbrack & \; \\{I_{2} = {{{Ln}( I_{Ave} )}\frac{{\mu_{2}( E_{eff} )}{d( {1 - \gamma} )}}{{{\mu_{1}( E_{eff} )}d} + {{\mu_{2}( E_{eff} )}{d( {1 - \gamma} )}}}}} & (20)\end{matrix}$

Furthermore, obtained information μ₁dγ may be set as a pixel value (afirst pixel value) of a bone and obtained information μ₂d(1−γ) may beset as a pixel value (a second pixel value) of fat. By displaying thevalue μdγ, degrees of attenuation of radiation in the individualsubstances may be visualized. For example, if bone density and fatdensity may not be obtained or are unknown, the thicknesses d of thesubstances included in the subject may be multiplied by the density ρ soas to obtain a value ρd instead of dγ. It is assumed that firstinformation on a thickness and density of the first constitutivesubstance is represented by “ρ_(i)d₁” and second information on athickness and density of the second constitutive substance isrepresented by “ρ₂d₂”. By displaying the value ρd, area densities of theindividual substances may be visualized. For example, “ρ₁d₁” mayvisualize distribution of bone density. Furthermore, in a case where thebone density and fat density may be obtained or estimated by differentmethods, the individual thicknesses dγand d(1−γ) may be determined as apixel value of the hone (the first pixel value) and a pixel value of thefat (the second pixel value). In this way, two-dimensional distributionsof the thicknesses of the individual substances may be visualized.

Hereinafter, a radiation imaging apparatus and a radiation imagingsystem which are suitable for obtaining pixel values to be used in thepresent invention will be described.

First, the radiation imaging system will he described with reference toFIG. 7. FIG. 7 is a block diagram schematically illustrating theradiation imaging system. Note that configurations the same as thoseillustrated in FIGS. 1 and 5 are denoted by reference numerals the sameas those illustrated in FIGS. 1 and 5 in this embodiment, and detaileddescriptions thereof are omitted.

A detector 101 may include a pixel array 102 including pixels in amatrix which convert radiation or light into electric signals, a drivingcircuit 103 which drives the pixel array 102, and an output circuit 104which outputs the electric signals supplied from the driven pixel array102 as image signals. The pixel array 102 includes the plurality ofpixels which output electric signals corresponding to incident radiationso as to obtain pixel values corresponding to the radiation, and theplurality of pixels are preferably arranged in a matrix. Each of theplurality of pixels may include a photoelectric conversion element and apixel circuit unit. The photoelectric conversion element converts lightwhich has been converted from the radiation by a scintillator intocharge, and a photodiode disposed on a semiconductor substrate, such asa silicon substrate, is used as the photoelectric conversion element.However, the present invention is not limited to this. A photoelectricconversion element of amorphous silicon disposed on an insulatedsubstrate, such as a glass substrate, or a conversion element whichdirectly converts radiation into charge without using a scintillator maybe used, for example. A controller 107 of a radiation imaging apparatus10 controls various units included in the radiation imaging apparatus 10in response to control signals supplied from the computer 13. Thedetector 101 of the radiation imaging apparatus 10 outputs an imagesignal corresponding to the radiation emitted from the radiationgeneration apparatus 11 controlled by the radiation control apparatus12. The output image signal is transmitted to the computer 13 afterbeing subjected to image processing, such as offset correction,performed by a signal processor 105. Here, a general wirelesscommunication or a general wired communication is used in thetransmission. The transmitted image signal is subjected to requiredimage processing performed by the computer 13 before being displayed ina display unit (not illustrated) of the computer 13.

Note that embodiments of a system, an apparatus, a method, a program ora storage medium, and the like may be employed in the present invention,for example. Specifically, the present invention may be applied to asystem including a plurality of devices or an apparatus including asingle device. Furthermore, although the processes described above arepreferably performed in accordance with programs, all or some of theprocesses may be performed by a circuit. Alternatively, the processesmay be performed by the signal processor 105 instead of the computer 13or may be performed utilizing both of the signal processor 105 and thecomputer 13. That is, the information processing unit and/or theinformation processing apparatus according to the present inventioncorresponds to at least one of the signal processor 105, the computer13, and a combination of the signal processor 105 and the computer 13.

The present invention is also realized by executing processing below.That is, software (programs) which realizes the functions of theforegoing embodiments is supplied to a system or an apparatus through anetwork or various storage media. Then a computer (or a CPU, an MPU, aCPU, or the like) included in the system or the apparatus reads andexecutes the programs.

Other Embodiments

Embodiments of the present invention can also be realized by a computerof a system or apparatus that reads out and executes computer executableinstructions (e.g., one or more programs) recorded on a storage medium(which truly also be referred to more fully as anon-transitorycomputer-readable storage medium’) to perform the functions of one ormore of the above-described embodiments and/or that includes one or morecircuits (e.g., application specific integrated circuit (ASIC)) forperforming the functions of one or more of the above-describedembodiments, and by a method performed by the computer of the system orapparatus by, for example, reading out and executing the computerexecutable instructions from the storage medium to perform the functionsof one or more of the above-described embodiments and/or controlling theone or more circuits to perform the functions of one or more of theabove-described embodiments. The computer may comprise one or moreprocessors (e.g., central processing unit (CPU), micro processing unit(MPU)) and may include a network of separate computers or separateprocessors to read out and execute the computer executable instructions.The computer executable instructions may be provided to the computer,for example, from a network or the storage medium. The storage mediummay include, for example, one or more of a hard disk, a random-accessmemory (RAM), a read only memory (ROM), a storage of distributedcomputing systems, an optical disk (such as a compact disc (CD), digitalversatile disc (DVD), or Blu-ray Disc (BD)™), a flash memory device, amemory card, and the like.

While the present invention has been described with reference toexemplary embodiments, it is to be understood that the invention is notlimited to the disclosed exemplary embodiments. The scope of thefollowing claims is to be accorded the broadest interpretation so as toencompass all such modifications and equivalent structures andfunctions.

This application claims the benefit of Japanese Patent Application No.2015-215209, filed Oct. 30, 2015, which is hereby incorporated byreference herein in its entirety.

REFERENCE SIGNS LIST

101 Detector

105 Signal processor

13 Computer

1. A radiation imaging system comprising: a detector including aplurality of pixels which obtain pixel values corresponding to incidentradiation transmitted through a subject; and an information processingunit configured to perform a process of estimating information onthicknesses of substances included in the subject using pixel values ofan arbitrary one of the plurality of pixels, an average value of energyof radiation quanta of the arbitrary pixel calculated in accordance withthe pixel values of the arbitrary pixel, a first table indicating therelationship between the pixel values of the arbitrary pixel and thethicknesses of the substances included in the subject, and a secondtable indicating the relationship between the average value of theenergy of the radiation quanta of the arbitrary pixel and thethicknesses of the substances included in the subject.
 2. The radiationimaging system according to claim 1, wherein the information processingunit includes: a first calculation unit configured to calculate anaverage of the pixel values of the arbitrary one of the plurality ofpixels based on the pixel values of the arbitrary pixel, a secondcalculation unit configured to calculate an average value of the energyof the radiation quanta of the arbitrary pixel in accordance withvariance of the pixel values of the arbitrary pixel calculated using thepixel values of the arbitrary pixel and an average of the pixel valuesof the arbitrary pixel calculated by the first calculation unit, and anestimation unit configured to estimate information on the thicknesses ofthe substances included in the subject using the average of the pixelvalues of the arbitrary pixel calculated by the first calculation unit,the average value of the energy of the radiation quanta of the arbitrarypixel calculated by the second calculation unit, the first table, andthe second table.
 3. The radiation imaging system according to claim 2,wherein the first table indicates the relationship among the average ofthe pixel values of the arbitrary pixel, the thicknesses of thesubstances included in the subject, and a mix ratio between thesubstances included in the subject, the second table indicates therelationship among the average value of the energy of the radiationquanta of the arbitrary pixel, the thicknesses of the substancesincluded in the subject, and the mix ratio between the substancesincluded in the subject, and the estimation unit estimates informationon the thicknesses of the substances included in the subject and the mixratio.
 4. The radiation imaging system according to claim 3, wherein theimage processing unit further includes a pixel value generation unitconfigured to generate pixel values of the substances in accordance withthe estimated information on the thicknesses of the substances and themix ratio.
 5. The radiation imaging system according to claim 4, whereinthe pixel value generation unit includes a first pixel value generationunit configured to generate a first pixel value which is a pixel valueof a first constitutive substance based on first information on athickness of the first constitutive substance and the mix ratio andincludes a second pixel value generation unit configured to generate asecond pixel value which is a pixel value of a second constitutivesubstance based on second information on a thickness of the secondconstitutive substance and the mix ratio.
 6. The radiation imagingsystem according to claim 5, wherein, when a linear attenuationcoefficient obtained when radiation energy of the first constitutivesubstance in the two different substances included in the subject isrepresented by “E[kev]” is denoted by “ρ₁(E)”, a linear attenuationcoefficient obtained when radiation energy of the second constitutivesubstance in the two substances is represented by “E[kev]” is denoted by“μ₂(E)”, a thickness of the subject is denoted by “d”, a mix ratio ofthe first constitutive substance is denoted by “γ”, an arbitrarycoefficient for conversion of the energy into a pixel value is denotedby “β”, the first pixel value is denoted by “I₁”, and the second pixelvalue is denoted by “I₂”, the pixel value generation unit generates apixel value of at least one of the substances by performing at least oneof the following calculations:I ₁=β∫₀ ^(∞) n(E)e ^(−μ) ¹ ^((E)dγ) EdEandI ₂=β∫₀ ^(∞) n(E)e ^(−μ) ² ^((E)d(1−γ)) EdE
 7. The radiation imagingsystem according to claim 5, wherein, when effective energy of theradiation is denoted by “E_(eff)”, a linear attenuation coefficientobtained when effective energy of the radiation of the firstconstitutive substance in the two different substances included in thesubject is represented by “E_(eff)[kev]” is denoted by “μ₁(E_(eff))”, alinear attenuation coefficient obtained when effective energy of theradiation of the second constitutive substance in the two substances isrepresented by “E_(eff)[kev]” is denoted by “μ₂(E_(eff))”, a thicknessof the first constitutive substance is denoted by “d₁”, a thickness ofthe second constitutive substance is denoted by “d₂”, a mix ratio of thefirst substance is denoted by “γ”, an arbitrary coefficient forconversion of the energy into a pixel value is denoted by “β”, the firstpixel value is denoted by “I₁”, and the second pixel value is denoted by“I₂”, the pixel value generation unit generates a pixel value of atleast one of the substances by performing at least one of the followingcalculations:I ₁ =βe ^(−μ) ¹ ^((E) ^(eff) ^()d) ¹ ^(γ)andI ₂ =βe ^(−μ) ² ^((E) ^(eff) ^()d) ² ^((1−γ))
 8. The radiation imagingsystem according to claim 5, wherein, when effective energy of theradiation is denoted by “E_(eff)”, a linear attenuation coefficientobtained when effective energy of the radiation of the firstconstitutive substance in the two different substances included in thesubject is represented by “E_(eff)[kev]” is denoted by “μ₁(E_(eff))”, alinear attenuation coefficient obtained when effective energy of theradiation of the second constitutive substance in the two substances isrepresented by “E_(eff)[kev]” is denoted by “μ₂(E_(eff))”, a thicknessof the subject is denoted by “d”, a mix ratio of the first substance isdenoted by “γ”, an arbitrary coefficient for conversion of the energyinto a pixel value is denoted by “β”, a calculated arithmetic average ofthe pixel values of the arbitrary pixel is denoted by “I_(Ave)”, thefirst pixel value is denoted by “I₁”, and the second pixel value isdenoted by “I₂”, the pixel value generation unit generates a pixel valueof at least one of the substances by performing at least one of thefollowing calculations:$I_{1} = {{{Ln}( I_{Ave} )}\frac{{\mu_{1}( E_{eff} )}d\; \gamma}{{{\mu_{1}( E_{eff} )}d\; \gamma} + {{\mu_{2}( E_{eff} )}{d( {1 - \gamma} )}}}\mspace{14mu} {and}}$$I_{2} = {{{Ln}( I_{Ave} )}{\frac{{\mu_{2}( E_{eff} )}{d( {1 - \gamma} )}}{{{\mu_{1}( E_{eff} )}d} + {{\mu_{2}( E_{eff} )}{d( {1 - \gamma} )}}}.}}$9. The radiation imaging system according to claim 4, wherein, when alinear attenuation coefficient obtained when radiation energy of thefirst constitutive substance in the two different substances included inthe subject is represented by “E[kev]” is denoted by “μ₁(E)”, a linearattenuation coefficient obtained when radiation energy of the secondconstitutive substance in the two substances is represented by “E[kev]”is denoted by “μ₂(E)”, a thickness of the subject is denoted by “d”, amix ratio of the first constitutive substance is denoted by “γ”, anarbitrary coefficient for conversion of the energy into a pixel value isdenoted by “β”, arbitrary monochromatic radiation energy is denoted by“E_(mono)”, and a pixel value of energy having an arbitrary spectrum isdenoted by “I(E_(mono))”, the pixel value generation unit generates thepixel value of the energy having the arbitrary spectrum by performingthe following calculation:I(E _(mono))=βe ^(−μ) ¹ ^((E) ^(mono) ^()d) ¹ ^(γ−μ) ² ^((E) ^(mono)^()d) ² ^((1−γ).)
 10. The radiation imaging system according to claim 1,wherein the information processing unit includes a first calculationunit configured to calculate an average of the pixel values of thearbitrary one of the plurality of pixels based on the pixel values ofthe arbitrary pixel, a second calculation unit configured to calculatean average value of the energy of the radiation quanta of the arbitrarypixel in accordance with variance of the pixel values of the arbitrarypixel calculated using the pixel values of the arbitrary pixel and anaverage of the pixel values of the arbitrary pixel calculated by thefirst calculation unit, and an estimation unit configured to estimateinformation on the thicknesses of the substances included in the subjectusing the average of the pixel values of the arbitrary pixel estimatedby performing a calculation using attenuation coefficients of thesubstances included in the subject, the average value of the energy ofthe radiation quanta of the arbitrary pixel estimated by performing acalculation using the attenuation coefficients of the substancesincluded in the subject, the first table, and the second table.
 11. Theradiation imaging system according to claim 10, wherein the first tableindicates the relationship among the estimated average of the pixelvalues of the arbitrary pixel, the thicknesses of the substancesincluded in the subject, and densities of the substances included in thesubject, the second table indicates the relationship among the estimatedaverage value of the energy of the radiation quanta of the arbitrarypixel, the thicknesses of the substances included in the subject, and athe densities of the substances included in the subject, and theestimation unit estimates information on the thicknesses and thedensities of the substances included in the subject.
 12. The radiationimaging system according to claim 11, wherein the image processing unitfurther includes a pixel value generation unit configured to generatepixel values of the substances in accordance with the estimatedinformation on the thicknesses and the densities of the substances. 13.The radiation imaging system according to claim 1, wherein the averagevalue of the energy of the radiation quanta is calculated using anamount of temporal and/or spatial change of a pixel value of thearbitrary pixel.
 14. An information processing apparatus that performs aprocess of estimating information on thicknesses of substances includedin a subject using pixel values of an arbitrary one of a plurality ofpixels which obtain pixel values corresponding to incident radiationtransmitted through the subject, an average value of energy of radiationquanta of the arbitrary pixel calculated in accordance with the pixelvalues of the arbitrary pixel, a first table indicating the relationshipbetween the pixel values of the arbitrary pixel and the thicknesses ofthe substances included in the subject, and a second table indicatingthe relationship between the average value of the energy of theradiation quanta of the arbitrary pixel and the thicknesses of thesubstances included in the subject.
 15. An information processing methodcomprising performing a process of estimating information on thicknessesof substances included in a subject using pixel values of an arbitraryone of a plurality of pixels which obtain pixel values corresponding toincident radiation transmitted through the subject, an average value ofenergy of radiation quanta of the arbitrary pixel calculated inaccordance with the pixel values of the arbitrary pixel, a first tableindicating the relationship between the pixel values of the arbitrarypixel and the thicknesses of the substances included in the subject, anda second table indicating the relationship between the average value ofthe energy of the radiation quanta of the arbitrary pixel and thethicknesses of the substances included in the subject.
 16. A programthat executes information processing on a radiation image and thatcauses a computer to perform a process of estimating information onthicknesses of substances included in a subject using pixel values of anarbitrary one of a plurality of pixels which obtain pixel valuescorresponding to incident radiation transmitted through the subject, anaverage value of energy of radiation quanta of the arbitrary pixelcalculated in accordance with the pixel values of the arbitrary pixel, afirst table indicating the relationship between the pixel values of thearbitrary pixel and the thicknesses of the substances included in thesubject, and a second table indicating the relationship between theaverage value of the energy of the radiation quanta of the arbitrarypixel and the thicknesses of the substances included in the subject.